Determining the structure of nonlinear models

Abstract

In order to perform systems analysis or synthesis, it is compulsory to deduce a model of the process. Articial Neural Networks ANN have shown their suitability to identify nonlinear dynamic processes without modelling them theoretically. Since no modelling is performed, the important issue for the Neural Network approach is to determine the required time delays. In this paper, di erent methods are presented that make it possible to reach this goal. First, some pruning methods are presented to detect nonrequired input neurons belonging to certain time delays. In order to avoid the high computational e orts of these methods, a new approach is presented which is based on the estimation of the gradient v ector of the system nonlinearity. All methods are applied to a continuous-stirred tank reactor.

Dynamic Fuzzy Systems for Qualitative Process Modeling: Principles of a New Systems Theory

“…The significance of the delayed outputs of lower than maximum order can be determined from the tangent planes. These are parallel to axis spanned by insignificant delayed outputs [7],…”

Identification of fuzzy relational models for fault detection

“…E Another method makes use of the analysis of a data gradient vector. Schultz and Hillenbrand (1997) have proposed a method for the determination of the relevant samples by examining the data gradient vector. This method can be extended in the case of noisy measurements, captured on real systems (Schultz & Krebs, 1997), but it does not allow a comparison of the relevance of di!erent signals.…”

“…10. E The last method is based on the approach of Schultz and Hillenbrand (1997). In this case, the best model is of second-order and reaches an error of "3.35;10\.…”